Final answer:
To determine the price an investor would pay for a share of Babble, Inc., one must calculate the present value of future dividends and divide by the number of shares. Assuming a 10% rate of return, the present value of dividends over three years totals to $53.84 million. Divided by 200 shares, the price per share is $269,200.
Step-by-step explanation:
To calculate what an investor would pay for a share of stock in Babble, Inc., we have to determine the present value of the future dividends because this will be the maximum price a rational investor is willing to pay. Since the company will disband in two years, we must discount all future dividends back to their present value. In this example, the profits (and therefore dividends) are expected to be $15 million immediately, $20 million one year from now, and $25 million two years from now.
To calculate the present value of the dividends, we use the formula for the present value of a future sum of money, which is: Present Value = Future Value / (1 + r)^n, where r is the discount rate (representing the required rate of return for the investor) and n is the number of periods until the payment.
Assuming an investor requires a 10% rate of return (just for illustration purposes), the present value of these dividends would be calculated as follows:
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- Present value of immediate dividend: $15 million / (1 + 0.10)^0 = $15 million
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- Present value of one-year dividend: $20 million / (1 + 0.10)^1 = $18.18 million
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- Present value of two-year dividend: $25 million / (1 + 0.10)^2 = $20.66 million
Adding these up gives us the total present value of all dividends: $15 million + $18.18 million + $20.66 million = $53.84 million.
Since there are 200 shares of stock, we then divide the total present value by the number of shares to find the price per share:
Price per share = $53.84 million / 200 shares = $269,200 per share.
This price represents what an investor would be willing to pay for a share of stock in Babble, Inc. under the given assumptions.